Constructing Confidence Intervals for μ1-μ2, When the sampling distribution for x̅1-x̅2 is approximated by a t-distribution and the population variances are not equal, you can construct a confidence interval for μ1-μ2 , as shown below.
construct the indicated confidence interval for μ1-μ2 . Assume the populations are approximately normal with unequal variances.
10K Race
To compare the mean finishing times of male and female participants in a 10K race, you randomly select several finishing times from both sexes. The results are shown at the left. Construct an 80% confidence interval for the difference in mean finishing times of male and female participants in the race. (Adapted from Great Race)

List the two conditions that must be met in order to use the paired-sample sign test.

In Exercises 23 and 24, (a) identify the claim and state Ho and Ha , (b) find the critical value(s) and identify the rejection region(s), (c) calculate d̄ and sd, (d) find the standardized test statistic t, (e) decide whether to reject or fail to reject the null hypothesis, and (f) interpret the decision in the context of the original claim. Assume the samples are random and dependent, and the populations are normally distributed.

A physical fitness instructor claims that a weight loss supplement will help users lose weight after two weeks. The table shows the weights (in pounds) of 9 adults before using the supplement and two weeks after using the supplement. At α=0.10, is there enough evidence to support the physical fitness instructor’s claim?

[APPLET] Teaching Methods

A new method of teaching reading is being tested on third grade students. A group of third grade students is taught using the new curriculum. A control group of third grade students is taught using the old curriculum. The reading test scores for the two groups are shown in the back-to-back stem-and-leaf plot.

At , α=0.10 is there enough evidence to support the claim that the new method of teaching reading produces higher reading test scores than the old method does? Assume the population variances are equal.

[APPLET] Teaching Methods

Two teaching methods and their effects on science test scores are being reviewed. A group of students is taught in traditional lab sessions. A second group of students is taught using interactive simulation software. The science test scores for the two groups are shown in the back-to-back stem-and-leaf plot.

At , α=0.01 can you support the claim that the mean science test score is lower for students taught using the traditional lab method than it is for students taught using the interactive simulation software? Assume the population variances are equal.

What conditions are necessary to use the dependent samples t-test for the mean of the differences for a population of paired data?

Test the claim about the mean of the differences for a population of paired data at the level of significance α. Assume the samples are random and dependent, and the populations are normally distributed.

Claim: μd<0 , α=0.05 , Sample statistics: d̄ =1.5 , sd=3.2 , n=14

Test the claim about the mean of the differences for a population of paired data at the level of significance α. Assume the samples are random and dependent, and the populations are normally distributed.

Claim: μd≤0 , α=0.10, Sample statistics: d̄ =6.5, sd=9.54, n=16

Constructing Confidence Intervals for μd To construct a confidence interval for μd , use the inequality below.

Construct the indicated confidence interval for μd . Assume the populations are normally distributed.

[APPLET] Drug Testing A sleep disorder specialist wants to test the effectiveness of a new drug that is reported to increase the number of hours of sleep patients get during the night. To do so, the specialist randomly selects 16 patients and records the number of hours of sleep each gets with and without the new drug. The table shows the results of the two-night study. Construct a 90% confidence interval for μd.